Question
Find the reciprocal of the complex number z = 9 – 4i.
Solution
We are given the complex number: z = 9 – 4i We are to find its reciprocal , i.e., 1 / z To find the reciprocal of a complex number, multiply numerator and denominator by the conjugate of the denominator: 1 / (9 – 4i) × (9 + 4i) / (9 + 4i) = (9 + 4i) / [(9 – 4i)(9 + 4i)] = (9 + 4i) / (9² + 4²) = (9 + 4i) / (81 + 16) = (9 + 4i) / 97 So: 1 / z = 9/97 + 4i/97
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